Group sparsity has shown great potential in various low-level vision tasks (e.g, image denoising, deblurring and inpainting). In this paper, we propose a new prior model for image denoising via group sparsity residual constraint (GSRC). To enhance the performance of group sparse-based image denoising, the concept of group sparsity residual is proposed, and thus, the problem of image denoising is translated into one that reduces the group sparsity residual. To reduce the residual, we first obtain some good estimation of the group sparse coefficients of the original image by the first-pass estimation of noisy image, and then centralize the group sparse coefficients of noisy image to the estimation. Experimental results have demonstrated that the proposed method not only outperforms many stateof-the-art denoising methods such as BM3D and WNNM, but results in a competitive speed.Index Terms-Image denoising, group sparsity residual constraint, group-based denoising, BM3D, WNNM.

Group-based sparse representation has shown great potential in image denoising. However, most existing methods only consider the nonlocal self-similarity (NSS) prior of noisy input image. That is, the similar patches are collected only from degraded input, which makes the quality of image denoising largely depend on the input itself. However, such methods often suffer from a common drawback that the denoising performance may degrade quickly with increasing noise levels. In this paper we propose a new prior model, called group sparsity residual constraint (GSRC). Unlike the conventional group-based sparse representation denoising methods, two kinds of prior, namely, the NSS priors of noisy and pre-filtered images, are used in GSRC. In particular, we integrate these two NSS priors through the mechanism of sparsity residual, and thus, the task of image denoising is converted to the problem of reducing the group sparsity residual. To this end, we first obtain a good estimation of the group sparse coefficients of the original image by pre-filtering, and then the group sparse coefficients of the noisy image are used to approximate this estimation. To improve the accuracy of the nonlocal similar patch selection, an adaptive patch search scheme is designed. Furthermore, to fuse these two NSS prior better, an effective iterative shrinkage algorithm is developed to solve the proposed GSRC model. Experimental results demonstrate that the proposed GSRC modeling outperforms many state-of-the-art denoising methods in terms of the objective and the perceptual metrics.Index Terms-Image denoising, group sparsity residual constraint, nonlocal self-similarity, adaptive patch search, iterative shrinkage algorithm.

Direction of arrival (DOA) estimation is an essential problem in the radar systems. In this paper, the problem of DOA estimation is addressed in the multiple-input and multiple-output (MIMO) radar system for the fast-moving targets. A virtual aperture is provided by orthogonal waveforms in the MIMO radar to improve the DOA estimation performance. Different from the existing methods, we consider the DOA estimation method with only one snapshot for the fast-moving targets and achieve the superresolution estimation from the snapshot. Based on a least absolute shrinkage and selection operator (LASSO), a denoise method is formulated to obtain a sparse approximation to the received signals, where the sparsity is measured by a new type of atomic norm for the MIMO radar system. However, the denoise problem cannot be solved efficiently. en, by deriving the dual norm of the new atomic norm, a semidefinite matrix is constructed from the denoise problem to formulate a semidefinite problem with the dual optimization problem. Finally, the DOA is estimated by peak-searching the spatial spectrum. Simulation results show that the proposed method achieves better performance of the DOA estimation in the MIMO radar system with only one snapshot.(DFT) [19] is used to estimate the DOA, where the received signals are sampled by the antennas in the spatial domain, and then the DOA estimation is equal to a corresponding frequency estimation in the transformed domain. erefore, the frequency (DOA) in the spatial domain is obtained by the DFT methods, but the resolution of DFT method is limited by Rayleigh criterion. e methods that can break through the Rayleigh criterion are called super-resolution methods. Multiple signal classification (MUSIC) method [20][21][22], Root-MUSIC [23], and the estimation of signal parameters via rotational invariant techniques (ESPRIT) method [24][25][26] are three most essential super-resolution methods. e noise subspace and signal subspace are obtained in the MUSIC and ESPRIT methods to estimate the DOA, respectively. A TOD-MUSIC algorithm is proposed in [27] to estimate the DOA in the scenario with low signal-to-noise ratio (SNR) with diversity bistatic MIMO radar.However, the subspaces are obtained from the estimated covariance matrix of the received signals, so the multiple measurements are needed in MUSIC and ESPRIT methods to achieve a reasonable estimation of the covariance matrix.

Compressed Sensing (CS) has been successfully utilized by many computer vision applications. However,the task of signal reconstruction is still challenging, especially when we only have the CS measurements of an image (CS image reconstruction). Compared with the task of traditional image restoration (e.g., image denosing, debluring and inpainting, etc.), CS image reconstruction has partly structure or local features. It is difficulty to build a dictionary for CS image reconstruction from itself. Few studies have shown promising reconstruction performance since most of existing methods employed a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) as the dictionary, which lack the adaptivity to fit image local structures. In this paper, we propose an adaptive sparse nonlocal regularization (ASNR) approach for CS image reconstruction. In ASNR, an effective self-adaptive learning dictionary is used to greatly reduce artifacts and the loss of fine details. The dictionary is compact and learned from the reconstructed image itself rather than natural image dataset. Furthermore, the image sparse nonlocal (or nonlocal self-similarity) priors are integrated into the regularization term, thus ASNR can effectively enhance the quality of the CS image reconstruction. To

No abstract